Skill Rolls
Skill rolls in Gearhead are open-ended: if you are sufficiently lucky, you can vaporize a Hunter-Destroyer using nothing but a broken herring. Each skill is based upon a stat. Your "score" for a particular skill roll is your rank in that skill, plus any bonuses or penalties, plus a stat bonus of (stat + 2) / 3. Thus, the minimum stat bonus is +1, and a stat of 10 will give +4. Your score is then looked up on a table, and a number of dice are rolled. If your score is more than 10, then you roll a d10 and d12 per 10, and the remaineder is looked up on the table as normal. The average total of the rolled dice is roughly equal to your score, plus score/10 (rounded up) times 2. So if you need to roll a 10 or better, you can expect to succeed about half the time if you have a score of 8. This is well and good, but the die-rolling system is open-ended: after the dice are selected as above and rolled, if a die lands on its largest number (i.e., 10 on a d10), the die is rolled again and added. And that's why, even when your opponents miss you 95% of the time and barely scratch you when they hit, you can still have your block knocked off by a single hit by a lucky Iron Monkey. An Example The minimum target roll for a critical hit is 25. (It can be higher if your opponent rolled an excellent defense, but he didn't do that this time.) You already hit your opponent. Your stats are Spot Weakness +8, Craft 14 (the relevant stat for Spot Weakness). There are no bonuses on the roll, so your score is 8 (skill) + 5 (stat) = 13. Looking at the chart, you will roll a d10 and a d12 for the first 10 of your score, and a d8 for the final 3. Your average roll for these dice is 18.34, so don't expect crits very often. You roll a 3 on the d12, a 9 on the d10, and an 8 on the d8. The 8 is rolled again, and you roll a 7. The total is 3 + 9 + 8 + 7 = 27, and you critically hit your opponent. Expected Values For the numbers-obsessed out there: the average result of an open-ended roll is the sum of each "side" on the dice, divided by the number of sides minus one. So an open-ended d4 will have an average roll of (1+2+3+4)/(4-1)=10/3. Thresholds for success rates For most purposes, skill roll results fall into three categories: almost never pass, pass sometimes, and almost always pass. If you're trying to open a door, almost never pass means you need to keep fooling with it until your fingers ache; pass sometimes means you maybe try once or twice, and almost always pass means you can count on getting through quickly (say under fire). If it's a "saving throw" type roll, well, you want "almost always pass". If it's a to-hit roll, you care what fraction are above a threshold. So, generally, quantiles are the important number. This table lists the score in the left column, and the difficulty level that yields a certain success rate in the other columns. These are based on about a hundred thousand simulated trials each.